Question

A box contains $100$ bulbs, out of which $10$ are defective. A sample of $5$ bulbs is drawn. The probability that none is defective is.

• A. ${\left(\frac{1}{10}\right)}^5$
• B. ${\left(\frac{1}{2}\right)}^5$
• C. $\left(\frac{9}{10}\right)$
• D. ${\left(\frac{9}{10}\right)}^5$

Answer 1

The correct option is D ${\left(\frac{9}{10}\right)}^5$

The probability that a bulb is defective $p=\frac{10}{100}=\frac{1}{10}$.
The probability that a bulb is not defective $q=1-p=\frac{9}{10}$
Thus out of 5 bulbs, the probability that none of the bulbs are defective
$=\frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}\times \frac{9}{10}$
$=(\frac{9}{10}{)}^5$